The 28-year-old center-back suffered an injury to his right captor in Real’s 2-0 win over Osasuna on Saturday.
He was forced to leave the pitch at half-time and now looks likely to miss the draw at Stamford Bridge.
Los Blancos will also be without Dani Carvajal due to the hamstring injury he suffered in the first leg last week, with the right-back expected to miss the rest of the season.
Zinedine Zidane could also be without Federico Valverde, who has not played since the 0-0 draw at Liverpool on April 14 after being diagnosed with coronavirus.
However, Real could replace Varane with captain Sergio Ramos after returning to training late last week. The 35-year-old defender has not played since playing for Spain at the end of March.
Marcelo is also expected to be available for the Spanish side, although he was selected to work at a polling station in the regional elections in Madrid on Tuesday.
Real drew 1-1 with Chelsea in the first leg in Madrid, meaning they need to improve that score in west London on Wednesday if they are to reach their first final since 2018.
Raiola: I think Real Madrid can afford Haaland
Mino Raiola says Real Madrid can afford to sign Erling Haaland this summer, despite the Spanish champions’ financial problems.
Real have reported debt of € 354.3million (£ 307million) in the fiscal year up to last June as finances have been affected by the coronavirus pandemic.
As Haaland announced a £ 66million release clause in his contract which will take effect next summer, Raiola and his father, Alf Inge Haaland, spoke to Barcelona and Real earlier this year.
The forward is expected to bring Borussia Dortmund over £ 100million if he sells him this summer and, when asked if Real could afford to buy him, Raiola said: “I don’t know ‘they can afford it, because I haven’t studied their books, but I think they can.
“I think they all can. The question is different: Can Madrid afford not to buy Haaland? What about Barça? “
“The [Haaland] needs to tell me when everything is clear and I can create a menu for him, and put things on his plate: we have this, that and the other.
“And at the moment, we can’t. What we do know today is that Dortmund spoke to us in an extremely solemn manner and said: “We are not selling him”. This is the situation, definitely.
“That’s what they said. Now let’s see if this desire is still there until September 1. “